Problem: Simplify the following expression: $\dfrac{3a^5}{2a^4}$ You can assume $a \neq 0$.
Answer: $ \dfrac{3a^5}{2a^4} = \dfrac{3}{2} \cdot \dfrac{a^5}{a^4} $ To simplify $\frac{3}{2}$ , find the greatest common factor (GCD) of $3$ and $2$ $3 = 3$ $2 = 2$ $ \mbox{GCD}(3, 2) = = 1 $ $ \dfrac{3}{2} \cdot \dfrac{a^5}{a^4} = \dfrac{1 \cdot 3}{1 \cdot 2} \cdot \dfrac{a^5}{a^4} $ $\phantom{ \dfrac{3}{2} \cdot \dfrac{5}{4}} = \dfrac{3}{2} \cdot \dfrac{a^5}{a^4} $ $ \dfrac{a^5}{a^4} = \dfrac{a \cdot a \cdot a \cdot a \cdot a}{a \cdot a \cdot a \cdot a} = a $ $ \dfrac{3}{2} \cdot a = \dfrac{3a}{2} $